In a small village there are two kinds of people: liars and truthtellers.
Everybody knows everybody and everybody knows as well who is a liar and who’s a truth-teller.
I approach six villagers and pose the same question to each of them:
"How many liars are among you?"

I get six distinct answers (integers, of course) and deduce the true one.

I agree with Charlie's solution just as written. With 6 different answers, there are 5 or 6 liars. If there were six, the answers would have been 0, 1, 2, 3, 4, 5, which is also consistent with 5 liars, so the truth cannot be deduced. Therefore, the answers were not 0, 1, 2, 3, 4, 5. Therefore, there were not 6 liars. Therefore, there were 5 liars. The answers must have been 5, 6 and four other numbers between 0 and 4.